1. Field of the Invention
The present invention relates to an analog-to-digital (A-D) converter suitable for a fuzzy controller, and more specifically to a successive approximation A-D converter suitable for use with a fuzzy control system.
2. Description of the Prior Art
There exist various analog-to-digital (A-D) converters. FIG. 1(A) shows a successive approximation (voltage comparison) A-D converter and FIG. 1(B) shows a successive approximation (current comparison) A-D converter, by way of example, which are of medium conversion speed type (several to several hundred microseconds) and suitable for high integration circuit, because the number of elements is relatively small.
In these drawings, the A-D converter roughly comprises a reference voltage generator 100, a D-A converter 200, a comparator 300, a controller 400, and a successive approximation register 500.
The D-A converter 200 converts a reference voltage V.sub.ref from the reference voltage generator 100 into a plurality of successively changing analog voltages V.sub.A in response to successively changing digital (m-bit) signals V.sub.D outputted from the successive approximation register 500. The successively changing analog voltages V.sub.A generated from the D-A converter 200 are compared with an analog input signal V.sub.in to be converted through the comparator 300. When one of the voltages V.sub.A generated from the D-A converter 200 is equal to or higher than the input signal V.sub.in (V.sub.A -V.sub.in &gt;0), the controller 400 outputs a reset signal S.sub.R to the successive approximation register 500 to determine one of the successively changing digital voltages V.sub.D as an A-D converted signal corresponding to the analog input signal V.sub.in. The above prior-art A-D converter is disclosed in "A-D, D-A CONVERSION TECHNIQUE IN MICROCOMPUTER AGE" page 75, published by NIKKAN KOGYO SHINBUN.
The fuzzy control system will be summarized hereinbelow. The concept of "fuzziness"has come about by considering what and how human beings think and how they communicate with one other. L. A. Zadeh proposed the concept of fuzzy sets in 1965. Research on fuzziness emphasizes that human knowledge is based on accumulated experience which can be generalized in the form of linguistic information such as know-how processed by specialists. This linguistic information generally proposed vagueness, obscurity, uncertainty, incompleteness or impreciseness, etc. represented by membership functions. The grade or value of the membership function is expressed by an actual numerical value (e.g. 0.7) lying between a region from "1" (YES) or "0" (NO). The fuzzy control is suitable for controlled objects difficult to be expressed by mathematical models.
With reference to FIG. 2, a fuzzy inference is executed in accordance with a plurality of rules expressed in the form of "if - then" rules as follows:
If x.sub.1 =A.sub.11 and x.sub.2 =A.sub.12, then y=A.sub.13 PA1 If x.sub.1 =A.sub.21 and x.sub.2 =A.sub.22, then y=A.sub.23 PA1 (e.g. if x.sub.1 =BIG and x.sub.2 =NORMAL, then y=SMALL) PA1 NL: Negative Large PA1 NM: Negative Medium PA1 NS: Negative Small PA1 ZR: Zero PA1 PS: Positive Small PA1 PM: Positive Medium PA1 PL: Positive Large
The above "if x.sub.1 =A.sub.11 and x.sub.2 =A.sub.12 " or "if x.sub.1 =A.sub.21 and x.sub.2 =A.sub.22 " is referred to as "antecedent" which indicates the conditions that the rules can be established, and "then y=A.sub.13 or y=A.sub.23 " is referred to as "consequent" which indicates the inferred result. The above x.sub.i are input signals (variables) generated by sensors for instance and y is referred to as an output control signal (variable) applied to an actuator for instance. Further, the above Aij are linguistic information or membership functions which define fuzzy rule propositions as follows:
The membership functions represent grades to which the input variables belong to a fuzzy set, and any given functions can be adopted for the membership functions. The membership functions of the antecedent can be formed into any given forms (such as normal distribution, triangular, singleton, etc.). The function value (grade) of the membership function lies within a range between g=1 and g=0, as already explained. Here, if two input signals (defuzzified value) x.sub.1.sup.o and x.sub.2.sup.o are given, each grade g can be obtained in accordance with each membership function. FIG. 2, shows an example of a fuzzy inference process, in which triangular membership functions are shown for simplification. When an input x.sub.1.sup.o is given, a function value gT.sub.11 of the membership function A.sub.11 can be obtained. In the same way, a function value gT.sub.12 of the membership function A.sub.12 can be obtained. Then, a MIN operation for selecting the smallest (smaller, in this example) one is executed for the above two function values gT.sub.11 and gT.sub.12. The executed MIN operation result is expressed as gT.sub.11.
Similarly, when the input x.sub.1.sup.o is given, a function value gT.sub.21 of the membership function A.sub.21 can be obtained. In the same way, a function value gT.sub.22 of the membership function A.sub.22 can be obtained. Then a MIN operation is executed for these two functions values gT.sub.21 and gT.sub.22. The executed MIN operation result is expressed as gT.sub.22.
A truncation between the obtained MIN operation result gT.sub.11 and the membership function A.sub.13 of the consequent of the rule 1 is executed to obtain a membership function y.sub.1 as shown by a shaded portion in FIG. 2. Similarly, a truncation between the obtained MIN operation result gT.sub.22 and the membership function A.sub.23 of the consequent of the rule 2 is executed to obtain a membership function y.sub.2 as shown by a shaded portion in FIG. 2.
A MAX operation for selecting the largest (larger, in this example) one is executed for the above two inferred results y.sub.1 and y.sub.2 to obtain a final defuzzified value. A final defuzzified value can be obtained by defuzzifying the final inferred (fuzzified) results by calculating a center of gravity thereof, for instance. The final defuzzified value is outputted as an output (defuzzified value) y.sub.0. Further detailed description is disclosed in NIKKEI ELECTRONICS No. 457, page 160, 1988 or by H. WATANABE et al "A VLSI Fuzzy Logic Controller with Reconfigurable, Cascadable Architecture" IEEE JOURNAL OF SOLID-STATE CIRCUITS, VOL. 25, No. 2, APRIL 1990.
Further, there exists the other method of obtaining the above-mentioned defuzzified value Y.sub.0. An example thereof is to calculate an average value as follows: ##EQU1## where gT denotes the minimum grade value of the antecedents of each rule and y denotes the value obtained when g=1 in the consequent membership function of each rule. This method is disclosed by M. Mizumoto "FUZZY CONTROLS UNDER VARIOUS DEFUZZIFIER METHODS", International Workshop on Fuzzy System Application, pages from 252 to 253, 1988.
FIGS. 3(A) and 3(B) show prior-art fuzzy controllers by way of example, in each of which the successive approximation A-D converters as explained already are incorporated with a fuzzy processor chip. In these fuzzy controllers, analog input signals A to D are converted into 6-bit digital signals; these digital signals are fuzzy-inferred by the fuzzy logic processor SRAM (static random access memory) in FIG. 3(A) or EPROM (erasable programmable read only memory) in FIG. 3(B); and 4-bit inferred results are converted again from digital to analog signals X and Y.
In other word, in the conventional fuzzy controller as described above, in spite of the fact that analog signals are usually inputted and outputted, since the signals are fuzzy-inferred by digital method, there exists a problem in that the scale of chip becomes large in size and further the actual inference speed is low and therefore the inference time (from when analog signals are inputted to when analog signal are outputted) is long. On the other hand, when the overall system is configured by analog circuits, it may be possible to simplify the circuit configuration. In this case, however, there exist other problems in that the analog system configuration is inferior to the digital system configuration in controller reliability, stability against noise, large-scale integration, low power consumption rate, etc.
Further, "Fuzzy controller" is disclosed in further detail in NIKKEI ELECTRONICS No. 457, on pages 157 to 168, 1988.